Chapter 1.9, Problem 6GP

Solution

year when at least $200$ teams participated in the robot-building competition.

There were at least $200$ teams participating in the year $1998$ to $2001$ .

Given information:

At least $200$ teams participated in the robot-building competition.

Calculation:

Consider the number of teams $T$ that have participated in a robot - building competition can be modeled by $T\left(x\right)=7.51x^2-16.4x+35.0;0\le x\le 9$ where $x$ is the number of years since $1992$ .

Need to determine in what years at least $200$ teams participated in the robot building competition.

Now, solve $T\left(x\right)\ge 200$

  $\begin{array}{c}7.51x^2-16.4x+35.0\ge 200\\ 7.51x^2-16.4x-165\ge 0\end{array}$

Let us graph $y=7.51x^2-16.4x-165$ and check where the graph cuts $x$ -axis.

The following diagram contains the graph of the equation $y=7.51x^2-16.4x-165$ on the domain $\left[0,9\right]$ .

  

Clearly, the graph lies above $x$ -axis when $5.9<x\le 9$ .

Therefore, there were at least $200$ teams participating in the year $1998$ to $2001$ .